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Letting $\\mathcal{A}_d \\subset (2d/(d-1), \\infty]$ be the set of exponents for which the constant functions on $\\mathbb{S}^{d-1}$ are the unique extremizers of this inequality, we show that: (i) $\\mathcal{A}_d$ contains the even integer"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.10365","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-28T01:10:58Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9def92f30d96729cb5bbbd115d011a7c7d687367a8a4ebed70c1351ce8205d4e","abstract_canon_sha256":"9139f8520d5d51472016862e73619e68c06d7819856d984228a4ea4ec854baeb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:18:22.952544Z","signature_b64":"GtHbWuSSrusNpi2wB7z1T/zCAGPY6QO7fh+GjHxogliA00osugCf7Hr4CQ8tAiG5S1WsB9AgdQcl8CmTigNNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9360729d819089db3f59d1d124de47bff8bb71040fbebae2f6a5ea8f17aaa07a","last_reissued_at":"2026-07-05T03:18:22.952195Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:18:22.952195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp mixed norm spherical restriction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Diogo Oliveira e Silva, Emanuel Carneiro, Mateus Sousa","submitted_at":"2017-10-28T01:10:58Z","abstract_excerpt":"Let $d\\geq 2$ be an integer and let $2d/(d-1) < q \\leq \\infty$. 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